A particular motor can provide a maximum torque of 110 N ? m. Assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to $8.13 \mathrm { rad } / \mathrm { s } ?$
A) 3.33 s
B) 2.83 s
C) 4.03 s
D) 4.36 s

Question

Quizplus · Accepted Answer

The correct answer is A.Explanation:The torque applied to the flywheel is:$$\tau = I \alpha$$where I is the moment of inertia of the flywheel and \alpha is the angular acceleration.The moment of inertia of a solid, uniform, cylindrical flywheel is:$$I = \frac{1}{2}MR^2$$where M is the mass of the flywheel and R is the radius.Substituting the given values into the equation for torque, we get:$$110 \text{ N} \cdot \text{m} = \frac{1}{2}(10.0 \text{ kg})(3.00 \text{ m})^2 \alpha$$Solving for \alpha, we get:$$\alpha = 3.87 \text{ rad/s}^2$$The angular acceleration is constant, so we can use the following equation to find the time it takes for the flywheel to accelerate from rest to $8.13 \text{ rad/s}$:$$\omega_f = \omega_i + \alpha t$$where $\omega_i$ is the initial angular velocity, $\omega_f$ is the final angular velocity, and t is the time.Substituting the given values into the equation, we get:$$8.13 \text{ rad/s} = 0 + 3.87 \text{ rad/s}^2 t$$Solving for t, we get:$$t = 2.10 \text{ s}$$Therefore, it will take 2.10 s for the flywheel to accelerate from rest to $8.13 \text{ rad/s}$.

A Particular Motor Can Provide a Maximum Torque of 110 8.13rad/s?8.13 \mathrm { rad } / \mathrm { s } ?8.13rad/s?

A Particular Motor Can Provide a Maximum Torque of 110 $8.13 \mathrm { rad } / \mathrm { s } ?$